Best Known (13, 13+29, s)-Nets in Base 81
(13, 13+29, 224)-Net over F81 — Constructive and digital
Digital (13, 42, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(13, 13+29, 298)-Net over F81 — Digital
Digital (13, 42, 298)-net over F81, using
- t-expansion [i] based on digital (12, 42, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(13, 13+29, 29336)-Net in Base 81 — Upper bound on s
There is no (13, 42, 29337)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 41, 29337)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 1 770330 922556 434274 396635 835406 866963 561583 514228 114987 930278 655875 306125 036641 > 8141 [i]